Deformation of $\Gamma_0(5)$-cusp forms

Avelin, Helen

doi:10.1090/s0025-5718-06-01911-9

Cited by 18 publications

(26 citation statements)

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“…A discussion of the generators of the groups Γ 0 (5), Γ 0 (5), Γ a,r and Γ a,r can be found in [FL05,§3], where a more general case is considered, and in [Ave03] where we have worked out the details for our special case. (Note that the parameters in [FL05] correspond to ours as a = b F L and r = 1/a F L .)…”

Section: Eisenstein Series On γ Armentioning

confidence: 99%

Computations of Eisenstein series on Fuchsian groups

Avelin

2008

Math. Comp.

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Abstract. We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z; s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real-valued rotation of E(z; s) as Re s = 1/2, Im s → ∞ and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z; s) when Re s > 1/2 near 1/2 and Im s → ∞, at least if we allow Re s → 1/2 at some rate. Furthermore, on non-arithmetic groups and for fixed s with Re s ≥ 1/2 near 1/2, our numerics indicate a Gaussian limit distribution for the appropriately normalized Fourier coefficients.

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Section: Eisenstein Series On γ Armentioning

confidence: 99%

Computations of Eisenstein series on Fuchsian groups

Avelin

2008

Math. Comp.

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“…[4,Avelin]) to a complex argument, K s (x), s ∈ C. The details of this algorithm are described in [64,Ch. 4].…”

Section: The Relations A)-c) Inmentioning

confidence: 99%

Computation of Maass waveforms with nontrivial multiplier systems

Strömberg

2008

Math. Comp.

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Abstract. The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group P SL(2, Z) with general multiplier systems and real weight. A selection of numerical results obtained with these algorithms is also presented. Certain operators acting on the spaces of interest are also discussed. The specific phenomena that were investigated include the Shimura correspondence for Maass waveforms and the behavior of the weight-k Laplace spectra for the modular surface as the weight approaches 0.

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“…Later, Bruggemen (1994) extended the algorithm of Maass waveform to other discrete cofinite subgroups of SL(2, R) [8]. Avelin (2003) and Farmer (2005) continue the study on the deformation of Maass cusp form. The deformed surface is represented by Teichmuller space T (s) and then they used Fricke involution to reduce the number of cusps to one for the congruence subgroup [9,10].…”

Section: Introductionmentioning

confidence: 99%